{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussian Transformation\n",
    "\n",
    "Some machine learning models like linear and logistic regression assume that the variables are normally distributed. Others benefit from \"Gaussian-like\" distributions, as in such distributions the observations of X available to predict Y vary across a greater range of values. Thus, Gaussian distributed variables may boost the machine learning algorithm performance.\n",
    "\n",
    "If a variable is not normally distributed, sometimes it is possible to find a mathematical transformation so that the transformed variable is Gaussian.\n",
    "\n",
    "\n",
    "### How can we transform variables so that they follow a Gaussian distribution?\n",
    "\n",
    "There are a few straightforward methods to transform variables so that they follow a Gaussian distribution. None of them is better than the other, they rather depend on the original distribution of the variables. They are:\n",
    "\n",
    "- logarithmic transformation\n",
    "- reciprocal transformation\n",
    "- square root transformation\n",
    "- exponential transformation (more general, you can use any exponent)\n",
    "- boxcox transformation\n",
    "\n",
    "To understand how the **boxcox** transformation works, please refer to these links:\n",
    "- http://www.statisticshowto.com/box-cox-transformation/\n",
    "- http://www.itl.nist.gov/div898/handbook/eda/section3/eda336.htm\n",
    "- http://onlinestatbook.com/2/transformations/box-cox.html\n",
    "\n",
    "\n",
    "In this notebook I will demonstrate all the transformations on the same variables for comparison, using the titanic dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Titanic dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "% matplotlib inline\n",
    "\n",
    "import pylab \n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Survived</th>\n",
       "      <th>Age</th>\n",
       "      <th>Fare</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>7.2500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>38.0</td>\n",
       "      <td>71.2833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>26.0</td>\n",
       "      <td>7.9250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>35.0</td>\n",
       "      <td>53.1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>8.0500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Survived   Age     Fare\n",
       "0         0  22.0   7.2500\n",
       "1         1  38.0  71.2833\n",
       "2         1  26.0   7.9250\n",
       "3         1  35.0  53.1000\n",
       "4         0  35.0   8.0500"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# load the numerical variables of the Titanic Dataset\n",
    "\n",
    "data = pd.read_csv('titanic.csv', usecols = ['Age', 'Fare', 'Survived'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Fill missing data with random sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# first I will fill the missing data of the variable age, with a random sample of the variable\n",
    "\n",
    "def impute_na(data, variable):\n",
    "    # function to fill na with a random sample\n",
    "    df = data.copy()\n",
    "    \n",
    "    # random sampling\n",
    "    df[variable+'_random'] = df[variable]\n",
    "    \n",
    "    # extract the random sample to fill the na\n",
    "    random_sample = df[variable].dropna().sample(df[variable].isnull().sum(), random_state=0)\n",
    "    \n",
    "    # pandas needs to have the same index in order to merge datasets\n",
    "    random_sample.index = df[df[variable].isnull()].index\n",
    "    df.loc[df[variable].isnull(), variable+'_random'] = random_sample\n",
    "    \n",
    "    return df[variable+'_random']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# fill na\n",
    "data['Age'] = impute_na(data, 'Age')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Age\n",
    "### Original distribution\n",
    "\n",
    "To visualise the distribution of the variable, Age in this case, we plot a histogram to visualise a bell-shape, and the Q-Qplot. Remember that if the variable is normally distributed, we should see a 45 degree straight line of the values over the theoretical quantiles. See the lecture \"Variable Distribution\" on section 4 for a description of Q-Q plots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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gM7ZjDjMZ2OTlffpAShZwKjy3GJAkVa2I+O5qxwCklL5fgNv/DPgW8LEGbb1S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\nX4fRo2HPPbMC7vOfL3cqSWqXLOIkSVJ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SjmWS/lVSr/Q1V9JzaX/f68LPz6xFLuLMzMzM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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x98bdaafe10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the histograms to have a quick look at the distributions\n",
    "# we can plot Q-Q plots to visualise if the variable is normally distributed\n",
    "\n",
    "def diagnostic_plots(df, variable):\n",
    "    # function to plot a histogram and a Q-Q plot\n",
    "    # side by side, for a certain variable\n",
    "    \n",
    "    plt.figure(figsize=(15,6))\n",
    "    plt.subplot(1, 2, 1)\n",
    "    df[variable].hist()\n",
    "\n",
    "    plt.subplot(1, 2, 2)\n",
    "    stats.probplot(df[variable], dist=\"norm\", plot=pylab)\n",
    "\n",
    "    plt.show()\n",
    "    \n",
    "diagnostic_plots(data, 'Age')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variable Age is almost normally distributed, except for some observations on the lower value tail of the distribution. Note the slight skew to the left in the histogram, and the deviation from the straight line towards the lower values ont he Q-Q- plot. In the following cells, I will apply the above mentioned transformations and compare the distributions of the transformed Age."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Logarithmic transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jvP560QN3++3wmc+UtwipGzHESZK0iIioj4hPRMSqwOPARRFxdhku/SGwc2Zu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\nSZIkST1iEidJkiRJPfJ/6TWEgfNi5nEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x98bdab4a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Logarithmic transformation\n",
    "data['Age_log'] = np.log(data.Age)\n",
    "\n",
    "diagnostic_plots(data, 'Age_log')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The logarithmic transformation, did not render a Gaussian like distribution for Age."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reciprocal transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JkgbzTJwkSQPdHBE3AF8vt38XuKmB9UiSNIAhTpKkCpn58Yh4H/Dmsqk7M7/T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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x98be9d9a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Reciprocal transformation\n",
    "data['Age_reciprocal'] = 1 / data.Age\n",
    "\n",
    "diagnostic_plots(data, 'Age_reciprocal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The reciprocal transformation was also not useful to transform Age into a variable normally distributed.\n",
    "\n",
    "### Square root transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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61yS1tFmzYN68LbeVmkA5ZAg8+2xt6pSqySZOkqQiUkpH5h+eGRG3ATsCP6tj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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x98bec64c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data['Age_sqr'] =data.Age**(1/2)\n",
    "\n",
    "diagnostic_plots(data, 'Age_sqr')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The square root transformation is a bit more succesful that the previous2 transformations, however, the variable is still not Gaussian, and this does not represent an improvement towards normality respect the original distribution of Age.\n",
    "\n",
    "### Exponential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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B7SpYUhPuu485K1qXQAkwalSJ65KK5HJKSZIKiIiHIuJP+a+HgUeBnxU5djuy\nBi6XUrohf/q5iNg9//ruwPNNjU0p1aWUhqSUhgwYMKD934gkAA48EE6Ia3lz+GG8zC4MY0nRDRzA\nggUlLE5qBWfiJEkq7HMNnm8CnksptbjZd2RTbpcDf0kp/bTBS7cAE4GZ+cebO7BWSc048IDEUX/5\nPhcxnbv5OMdwI2voX/T4wYNLWJzUSjZxkiQ1EhH98k9fa/TSOyOClNJLLbzFcGAC8FBE/DF/7myy\n5u1XEXEKsAo4vqNqltSMDRv45l9OYzKzmEMtp1BcAmW9iGwHAqmzsImTJGlbDwIJiCZeS8B7mhuc\nUrqnwFgA76qRyqim71quePVLTOZOzuNczudcCv/x3FbPnjB7NtTWlq5GqbVs4iRJaiSltE+la5DU\nfge/83F+81rrEigHD4aVK0tfm9QeNnGSJDUjInYF9gd2qD+XUrqrchVJKsp993HHa61PoHTZpKqB\nTZwkSQVExKnAN8i2FfgjMBRYAhxWybokNe/kna/l4nUTeZm9GcN8lvNPLY6JgKuvdtmkqoNbDEiS\nVNg3gI8Cq1JKI8k27X65siVJKiglvrfjRVyxbiy/56MMY0mLDdxuu2UbeL/1lg2cqodNnCRJhb2Z\nUnoTICK2Tyn9FXhvhWuS1JQNG+Dkk/nOm9OZQy2jWVDUFgL//u9lqE3qYC6nlCSpsKcjYhfgJuCO\niFhLtjWApE6kPoHysFYkULp8UtXMJk6SpAJSSsfkn54XEXcCfYHfVrAkSY20JYEypTIUJpWQTZwk\nSY1ExK3AXOCmlNLrACml31W2KknbWLKE2187il5s4nDu4C4+1eKQXXYpQ11SiXlPnCRJ2/olMAZ4\nIiJ+FRHHRETvShclKTN1KpwQ1/LmoSN5hb4MZWnRDdzatWUoUCoxmzhJkhpJKd2cUhoHDAauB04C\nnoyIKyPi8MpWJ3VvU09P7HLJRVxL8QmUkC2htIFTV+FySqmCaqbN3+r4jIM2ManRuXJYOXNM2T9T\nqgYppXXAtcC1EfEBYDZZQ9ezooVJ3dWGDXz0l19hMleS40RO5go2sH2Lw0aNKkNtUhk5EydJUgER\nMTAivh4R95IlVN4GfLjCZUnd09q1cMQRTE5Xch7nMp45RTdwCxaUoT6pjJyJkySpkYj4MjCObE+4\n64FvpZTuq2xVUveUy8F3xj/OfLIEylOZzdWc1OI4EyjVldnESZK0rWHA94GFKaW3Kl2M1F3lcvDz\n8UtYigknr44AAAAgAElEQVSUUkM2cZIkNZJSOrnSNUiCJf96LXcykafYmzHMLyrAxARKdQfeEydJ\nkqROZdddEmfHRfz8RRMopaY4EydJkqROY+ftNvCfm77Cya1MoJS6E5s4SZIaiYh+zb2eUnqpXLVI\n3ckZp6zlvzZ9icO4k/M4l/M5F4iixrqNgLoTmzhJkrb1IJDI/vY4CFibf74L8CSwT+VKk7qWnXaC\nN96AfdiSQHlSkQmU9dxGQN2NTZwkSY2klPYBiIhLgRtTSrfmjz8LHF3J2qSupL6BG8oSbm5lAqVb\nCKg7M9hEkqTChtY3cAAppd8Ah1awHqlLeeMNOI5fcScjeZV3MowlbiEgFcGZuC6uZtr8dr/HGQdt\nYlIHvI8kVaFnIuIcYE7+uBZ4poL1SFVvzz3hmWcAEmfxfS5iOnfzcY7hRtbQv8XxbiEgORMnSVJz\nxgEDgBuBG/LPx1W0IqmK1Tdw27GByzmFi5hOjhMZzYIWG7iU3EJAqudMnCRJBeRTKL8RETunlP5R\n6XqkavfMM7ALa7mOYxnFIs7nu5zHebSUQLnHHmUpT6oazsRJklRARBwaEY8Af8kffzAiLq5wWVJV\nmToVIrKvfXic+ziUT3A3JzGb8zifYhq41avLU6tULZyJkySpsP8LfAa4BSCl9L8R8cnKliRVj6lT\n4ZJLsuetSaA0eVJqnjNxkiQ1I6X0VKNTmytSiFSF6uqyx9YkUJo8KbXMJk6SpMKeiohDgRQR20XE\nN8kvrZTUss2bE9P4Pr/iBJYxhKEs5W+8t+D1Jk9KxbGJkySpsK8AXwX2BFYDB+ePJRWw557Z/W+9\nYwOXcSrf5+wWEyh79jR5UmoN74mTJKkJEdETmJBSqq10LVK1qN9CoLUJlFOmlK1EqUtwJk6SpCak\nlDYDJ1a6DqmaPPNM6xMoTz8dLjbzVWoVZ+IkSSrsnoj4OXAt8PY+cSmlP1SuJKnycjkYP37b8yZQ\nSuVhEydJUmEH5x8vaHAuAYdVoBapUyjUwB3Hr7iKk3iavRjD/GYDTCS1j02cJEkFpJRGVroGqbOZ\nPr3xmcQ0ZvJ9zuYehnM0NxUMMKl3wAElK0/qFrwnTpKkAiJiYERcHhG/yR8fEBGnVLouqRJGj85S\nJ1et2nJuO4pPoKx3wAHw8MMlLlbq4mziJEkqbBZwG7BH/vhvwL9WrBqpQkaPhoULtz7Xl5f5DZ/l\nFK7gfL7LeOawnh2aHJ/Sli8bOKn9bOIkSSqsf0rpV8BbACmlTcDmypYklV/jBq6GJ4pOoNxll9LX\nJ3U3LTZxEXFFRDwfEX9ucK5fRNwREcvzj7s2eO2siFgREY9GxGdKVbgkSWXwj4jYjSzMhIgYCrxS\n2ZKkyjqEpdzPIbybv3M4d3A1JxW8dpdd3MBbKoViZuJmAUc0OjcNWJhS2h9YmD8mIg4AxgIH5sdc\nnN8sVZKkavRvwC3AvhFxL3AV8PXKliSVVv29bw2/6h3Lr7mTkbzKOxnGkm22EGi4bDIlGzipVFps\n4lJKdwEvNTp9FDA7/3w2cHSD8/NSSutTSk8AK4CPdVCtkiSVVX4/uE8BhwKnAQemlP5U2aqk0mnq\n3rdMYhrf59ccz4N8hKEs3WYLgVGjylKiJNq+xcDAlNKz+ed/Bwbmn+8JLG1w3dP5c5IkVY2I+GKB\nl/4pIkgp3VDWgqQyaaqB68VG/h9f4RSuYC7jOJkrtgkwGTUKFiwoU5GS2r9PXEopRURq7biImAJM\nARg4cCCLFy9u1fjXX3+91WM6g3LXfcZBm9r9HgN37Jj3KbdqrLtSNbfn96R/FsunGmuGqq378/nH\nd5HNwi3KH48E7gNs4lT1pk6FSy5p/pq+vMz1fIlRLOICvsO5TQSYpFb/LVBSe7W1iXsuInZPKT0b\nEbsDz+fPrwb2bnDdXvlz20gp1QF1AEOGDEkjRoxoVQGLFy+mtWM6g3LXPWna/Ha/xxkHbeInD1Xf\nvvDVWHelal5ZO6LNY/2zWD7VWDNUZ90ppckAEXE7cED96pP8z7xZFSxN6hDFNHA1PMF8xrAfKziJ\n2c0GmEgqr7ZuMXALMDH/fCJwc4PzYyNi+4jYB9gfeKB9JUqSVDF7N7h9AOA5YFClipE6Sl1d868X\nm0DpfXBSZRSzxcA1wBLgvRHxdEScAswEDo+I5cDo/DEppYeBXwGPAL8FvppScj8dSVK1WhgRt0XE\npIiYBMwHvPNHVenAA7ekTW5u5m9nLSVQ1vM+OKlyWly3lVIaV+ClJv/tJaU0A5jRnqIkSeoMUkpf\ni4hjgE/mT9WllG6sZE1SWxx4IDzySEtXJc7kB8zkLO5hOEdzE2voD0DPnrCpum4zl7q06rphSJKk\nMsnvc7ogpTQSsHFTVWupgevFRi7hdE7l8iYTKKdMKXGBklqlrffESZLUpeVvB3grIvpWuhaplPry\nMr/lCE7lci7gO9SS26qBO/10uPjiChYoaRvOxEmSVNjrwEMRcQfwj/qTKaV/qVxJUmG5HEyc2Pw9\nbw01TqCcEyeR3iptjZLazyZOkqTCbsA94VQlcjkYP7746w9hKbfwBXqxiU9zO79jBKd/pXT1Seo4\nNnGSJBV2LbBf/vmKlNKblSxGas706cVfeyy/5ipOYjV7Mob5/I33umxSqiLeEydJUiMR0Ssifgg8\nDcwGrgKeiogfRsR2la1O3d3UqVu2Cmj4tWpVMaMTZzKTX3M8D/IRhrGUR9N7SckGTqomNnGSJG3r\nR0A/YJ+U0kdSSh8G9gV2AX5c0crUrU2dCpdc0raxvdjIpXyZmZzFXMYxmgXsPLh/xxYoqSxs4iRJ\n2tbngC+nlF6rP5FSehU4HTiyYlWp26ura9u4vrzMb/jsVgmUG2IHZrizr1SVvCdOkqRtpZRSauLk\n5ojY5rxULsWmTjbUMIFyIrO4ion07AmzZ0NtbcfXKKn0nImTJGlbj0TESY1PRsR44K8VqEfdWMN7\n4FrrEJZyP4dwwK5/p/edtzM7TSQl2LTJBk6qZs7ESZK0ra8CN0TEycCD+XNDgB2BYypWlbqd9twD\nV59A+cJ2e8CSW+G97+3Y4iRVjE2cJEmNpJRWA4dExGHAgfnTt6aUFlawLHVDbbsHLnEmP2AmZ/E/\nOx7Kh1bdBAMGdHRpkirI5ZSSJBWQUlqUUvrP/FfRDVxEXBERz0fEnxuc6xcRd0TE8vzjrqWpWtUq\nl4Ptt99624Bi74GLgJQgbdhIOiVLoGTsWD700kIbOKkLciZOEjXT5rd57BkHbWJSO8Y3tnLmmA57\nL6mCZgE/J9tfrt40YGFKaWZETMsfn1mB2tQJ5XIwfnzbxw8aBLz8Mhx7LCxcCOecA+efDz3893qp\nK7KJkySpg6WU7oqImkanjwJG5J/PBhZjE6e86dPbPjYCfvaNJ+DQMbBiBcyaBRMndlhtkjofmzhJ\nkspjYErp2fzzvwMDK1mMOpcnn2zbuF694L/OWcoR3/8CbNwIt98OI0Z0aG2SOh/n2CVJKrP8HnQF\n95uLiCkRsSwilr3wwgtlrEyVMHVqdj9bawwenI3ZeM11HDFzJLzjHbB0qQ2c1E3YxEmSVB7PRcTu\nAPnH5wtdmFKqSykNSSkNGWA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      "text/plain": [
       "<matplotlib.figure.Figure at 0x98bef04e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data['Age_exp'] = data.Age**(1/1.2) # you can vary the exponent as needed\n",
    "\n",
    "diagnostic_plots(data, 'Age_exp')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The exponential transformation is the best of all the transformations above, at the time of generating a variable that is normally distributed. Comparing the histogram and Q-Q plot of the exponentially transformed Age with the original distribution, I would say that by visual inspection the transformed variable follows more closely a Gaussian distribution. \n",
    "\n",
    "***Should I transform the variable?***\n",
    "\n",
    "It depends on what we are trying to achieve. If this was a situation in a business setting, I would use the original variable without transformation to train the model, as this would represent a simpler situation at the time of asking developers to implement the model in real life, and also it will be easier to interpret. If on the other hand this was an exercise to win a data science competition, I would opt to use the variable that gives me the highest performance.\n",
    "\n",
    "\n",
    "### BoxCox transformation\n",
    "\n",
    "The Box-Cox transformation is defined as: \n",
    "\n",
    "T(Y)=(Y exp(λ)−1)/λ\n",
    "\n",
    "where Y is the response variable and λ is the transformation parameter. λ varies from -5 to 5. In the transformation, all values of λ  are considered and the optimal value for a given variable is selected.\n",
    "\n",
    "Briefly, for each  λ (the transformation tests several λs), the correlation coefficient of the Probability Plot (Q-Q plot below, correlation between ordered values and theoretical quantiles) is calculated. \n",
    "\n",
    "The value of λ corresponding to the maximum correlation on the plot is then the optimal choice for λ.\n",
    "\n",
    "In python, we can evaluate and obtain the best λ with the stats.boxcox function from the package scipy.\n",
    "\n",
    "Let's have a look."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal λ:  0.764852250028\n"
     ]
    },
    {
     "data": {
      "image/png": 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HQErpgepVJKkjgwfDu9Z1LoEyAq67zmmTqg82cZIkFRERnwXOJltW4JfAGGAp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\nF1TutZX8+divTAW8BOzT4v7b8tu2Sik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      "text/plain": [
       "<matplotlib.figure.Figure at 0x98bef9aac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data['Age_boxcox'], param = stats.boxcox(data.Age) \n",
    "\n",
    "print('Optimal λ: ', param)\n",
    "\n",
    "diagnostic_plots(data, 'Age_boxcox')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Box Cox transformation was as good as the exponential transformation we performed above to make Age look more Gaussian. Whether we decide to proceed with the original variable or the transformed variable, will depend of the purpose of the exercise as described above.\n",
    "\n",
    "Let's check at another variable\n",
    "\n",
    "## Fare\n",
    "\n",
    "### Original distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mjgHmletExFjgdIrJVCcBV5QvlkuS1GciYkhEfAV4ErgS+D7wRER8JSKc7FuS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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x98beede898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diagnostic_plots(data, 'Fare')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variable Fare is very skewed, with the majority of the values accumulated on the lower Fare range, and just a few observations who paid a high Fare to get on the Titanic. As expected, in the Q-Q plot we observe a big deviation of the observed data from the 45 degree red line."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Logarithmic transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iB8yeYfdJdSxb4iRJKlFEbBURd0TE44Xvn4qIU/OuS1I+Bg/OJjbZiT/TQB1b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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x98be8d3d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Logarithmic transformation\n",
    "data['Fare_log'] = np.log(data.Fare+1) # We don't want log of 0\n",
    "\n",
    "diagnostic_plots(data, 'Fare_log')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The logarithmic transformation does a good job to make the variable Fare look more Gaussian. The histogram still shows signs of skewness and some observations deviate from the 45 degree line on the Q-Q plot, but by all means it is much more Gaussian looking than the original variable.\n",
    "\n",
    "### Reciprocal transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1lX3CECdJagYnA9Mj4m+Bu8q2UcAGwBE1q0qStGaZ8PvfF8Ft6lRYsKB4ru2o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\nEVEj/wUtq9oCGxjsfQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x98bdf2a6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Reciprocal transformation\n",
    "data['Fare_reciprocal'] = 1 / (data.Fare+1)\n",
    "\n",
    "diagnostic_plots(data, 'Fare_reciprocal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The reciprocal transformation, on the other hand, is not useful to make Fare less skewed.\n",
    "\n",
    "### Square root"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7so6TDz+chbfbb4c997TjZA1yJE6SpDwiYqeImAE8k/u8bURMamU3SSqJ+nro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\nljcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x98bf092c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data['Fare_sqr'] =data.Fare**(1/2)\n",
    "\n",
    "diagnostic_plots(data, 'Fare_sqr')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The square root transformation is not useful to make Fare more Gaussian looking.\n",
    "\n",
    "### Exponential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LP0VSh5MJ48bBBhvA3/8Oxx0HU6fCoEGsuGLDp0OR+VwLTq2h9eZOlySpOg2n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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x98be7c2828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data['Fare_exp'] =data.Fare**(1/5)\n",
    "\n",
    "diagnostic_plots(data, 'Fare_exp')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The exponential transformation works better than the last 2, perhaps as well as the logarithmic transformation.\n",
    "\n",
    "### BoxCox"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal lambda:  -0.0977870289385\n"
     ]
    },
    {
     "data": {
      "image/png": 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6ZYAbr0uXol9S0ioY4iRJylNEHLSaQ1+KCFJK1xdwre7AN4AHV3Fs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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x98be8fd390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data['Fare_boxcox'], param = stats.boxcox(data.Fare+1) # you can vary the exponent as needed\n",
    "\n",
    "print('Optimal lambda: ', param)\n",
    "\n",
    "diagnostic_plots(data, 'Fare_boxcox')"
   ]
  },
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    "We can see that after the transformation, the quantiles are somewhat more aligned over the 45 degree line with the theoreical quantiles of the Gaussian distribution."
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "For Fare, we could use the logarithmic, exponential or Box-Cox transformation to shape the variable into a transformed version that follows more closely (albeit not perfectly) a normal distribution. It is very likely that this transformation would improve the performance of many machine learning models, respect to using the variable Fare without transformation. Go ahead and test this transformation on a few machine learning algorithms, using the original Fare and the transformed version for comparison."
   ]
  },
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